Judge Diane Kottmyer said in her decision, filed on April 17 in the court clerk's office, that Entwistle's lawyers did not prove they needed money to hire the expert.

Entwistle, 29, is accused of killing his wife, Rachel, 27, and daughter, Lillian Rose, 9 months, on Jan. 20, 2006 in their bedroom at the 6 Cubs Path home they rented in Hopkinton.

The motion filed by Entwistle's lawyers, Elliot Weinstein and Stephanie Page, was impounded and not available to the public, but Kottmyer's decision was.

"Counsel cite no case in which a motion for funds has been allowed to retain experts to assist in the selection of a jury,'' she said in her decision. "They argue that it is essential to develop a questionnaire to 'help identify overt, subtle and hidden bias of prospective jurors.' They point out that the present case has received extensive local, national and international publicity.''

Kottmyer disputed that argument.

"But many criminal cases receive substantial publicity in the location in which the events leading to the charges took place,'' she said. "In most of these cases, that is the same geographical area from which jurors are selected.''

Kottmyer said it is the court's job to make sure jurors follow instructions about disregarding pre-trial and trial publicity.

Entwistle is being held without bail at the Middlesex Jail in Cambridge. His trial is scheduled to start on June 2 at the new courthouse in Woburn.

Authorities say he killed his wife and daughter with a gun he stole from his in-laws' Carver home to hide his life of debt, online business scams and sex.

He then drove to Carver, returned the gun to where it had been stored and flew to England, returning to his parents' Nottinghamshire home. He was later arrested there and extradited to Massachusetts to face trial.

Entwistle is charged with two counts of first-degree murder and the illegal possession of a firearm. If convicted, he faces a mandatory life sentence without the possibility of parole.